This report presents a study of irregular structures near collapse, aimed to understand better the influence of irregularities and adequacy of simplified techniques of analyses to real behavior of such structures. Experience shows that buildings with irregularities are prone to severe damage as demonstrated in many earthquake occurrences. An experimental study was focused on the validation of the analytical tools for evaluation of seismic response of irregular structures, i.e. setback structures. A number of analytical studies had been carried out to evaluate such structures, but very few experimental works had been done on this subject. Equally important scope of this study was the design of a structural model for study of structural systems near collapse. A versatile reconfigurable structural model was developed to be used and reused with structures undergoing severe damage to sacrificial elements thus capable to be repaired and further tested without complete collapse. The model was developed with two independent support systems: one for gravity loads and one for lateral loads. Loss of the lateral load resisting system which may happen during earthquakes does not damage the vertical load resisting system (named also gravity columns) thus preventing collapse. The model was designed as a one-third scale three-story three-bay steel frame structure. For the purpose of this study, the irregularity aspect was introduced to the designated model by having two unequal towers creating a setback structure. From dynamic simulation of the analytical model, a ground motion history (Northridge 1996, Rinaldi RS), from the SAC project with 10% probability of exceedence in 50 years in Los Angeles, was selected to perform physical (using shake table testing) and computational simulations.